Binary Logic: Concepts & Tricks

In Binary Logic questions, you find people answer a question in two or three different statements. Some of these statements are true while others are false. Based on the given data, you need to figure out the actual category of persons. Generally, there are three types of people:
  1. Truth-Speaker: All statements given by him are true.He always speaks the truth.
  2. Lie-teller: A Lie teller always tells a lie.
  3. Switcher: The Switcher switches between the lie and the truth. If the first statement of switcher is false, then his second is true, next statement i.e. third is false and fourth is true and this goes on. Similar pattern will follow if he starts from truth i.e. if the first statement of switcher is true, then his second is false, next statement i.e. third is truth and fourth is false and this goes on. The total number of true /false statements are not fixed but an order is fixed i.e if he starts from false it is FALSE-TRUE-FALSE…and if he starts from truth it is TRUE-FALSE-TRUE.
To solve questions on Binary logic, we have to make certain assumptions. If there is some contradiction while solving question with the assumption, then that assumption is wrong and  if there is no contradiction then that assumption is correct and  hence the solution
Technique to solve:
Step 1: There are some statements which help us to solve the binary logic questions easily. With the help of these statements, we can identify the people, without making any assumption. Broadly, there are four types of statements which we should look for. If someone makes any of these statements we can find their category. This can be clearly understood as given below:
  1. The first statement we should look for is "I am a Lie-teller":
    Now if we assume that if a person is saying, "I am a Lie-Teller" is a Truth-Speaker then it is not true as the only statement a Truth-Speaker can say is  "I am a Truth-Speaker". So, we can conclude that the person who said "I am a Lie-teller" is not the Truth-Speaker.
    If we assume that if a person saying, "I am a Lie-teller" is a lie teller then it is also not true as the only statement a lie teller can say is "I am a Truth-Speaker"
    So we can conclude that the statement “I am a Lie-teller” can be made only by a Switcher. Further, the switcher is not a Lie teller and he can give both true and false statement. Since this statement is false so his next statement will be truth. This will help us to solve the question further.
  2. The second statement we should look for is" I am not a truth teller":
    Similar to the above explanation, this statement cannot be given by a Truth-Speaker as if he gives this statement then it is a lie which is not in line with the fact that a Truth-Speaker always speaks the truth.
    Further, if the Lie-teller makes the above statement, then it will be the truth for him which again goes against the fact that a Lie-teller will always lie. So, a Lie-teller cannot make this statement.
    Now the switcher can say “I am not a Truth-Speaker “as he can speak the truth and as well as can tell the lie. So it is true for him. As he switches between truth and lie,so his next statement is a lie. This will help us to solve the question further.
  3. The third statement we should look for is "I am a Switcher":
    We can conclude the following
    1. truth teller cannot make this statement as by saying this he will be telling a lie.
    2. lie teller and switcher can make this statement.
    Now for switcher, this statement is true, so his next statement will be false.
  4. The fourth statement we should look for is “I am not a Switcher”:
    We can conclude the following
    1. The switcher can make this statement when his turn of making statement is false.Now for switcher this statement is false, so his next statement will be true.
    2. Truth speaker can make this statement as it will be a true statement for him.
    3. Lie teller cannot make this statement as it will be a true statement for him and he has to tell a lie.
Summarize:
Statement Made by Truth or lie
I am a Lie-teller Switcher Lie
I am not a Truth-Speaker Switcher Truth
I am a Switcher Lie-teller or Switcher Lie for Lie-teller, truth for Switcher
I am not a Switcher Truth-Speaker or Switcher Lie for Switcher, truth for Truth-Speaker
Consider the following example:
Three boys- Ashish, Bhanu and Chintu replied to the question, "Who among you is a Doctor?" in the following manner:
We know that exactly one of these boys is a Doctor, one is a Painter and one is an Athlete.  Also, one of them always speaks the truth, one always lies and one alternates between the truth and the lie.
Ashish: Bhanu: Chintu:
I am a Doctor Chintu is an Athlete I am not a Painter
Bhanu is a Painter Ashish is not a Doctor Bhanu is not a painter
I am an  Switcher I am a Lie-teller Ashish is a Lie-teller
In the above question, Bhanu makes the statement, “I am a Lie-teller”, which implies that Bhanu is a Switcher. Also, Ashish said that he is a Switcher, which implies that he can be either a Lie-teller or a Switcher. Now, since Bhanu is the Switcher, Ashish is definitely the Lie-teller. This leaves us with Chintu as the Truth-Speaker. Since Bhanu is the Switcher, so the statements following/preceding the statement, “I am a Lie-teller” are true, we can conclude that Ashish is not a Doctor. Also as Chintu is a Truth-Speaker, according to his statements, Bhanu is not a painter and he himself is not a painter, thus Ashish is the painter. Now, Bhanu’s first statement is a lie (since third statement is also a lie, so the order for Bhanu’s statements will be 1st-false,2nd-true,3rd-false). This means Chintu is not an athlete, which leaves us with the only option for Chintu as Doctor and Bhanu as an athlete. 
Ashish Bhanu Chintu
Lie-teller Switcher Truth-Speaker
Painter Athlete Doctor
Therefore, the answer to the question, ‘Who is a Doctor’, is Chintu.
If we consider the statement like “I am a Truth-Speaker it is not of much use as truth speaker, lie teller and switcher all three can give this statement.
Step 2: Now what if we do not have any of the above said 4 statements in any of the statements. In that case we will self assume their status and the assumption in which there is no contradiction will be the answer.
Now, consider the following example:
Uday, Ramesh and Suresh made the following statements regarding the type of vehicle they own. Each one of them belongs to one category of Truth-Speaker, Lie-teller or Switcher. Only one among them is a Truth-Speaker. Further, each of them own a different vehicle and each of them own exactly one among car, cycle and bike.
Uday Ramesh Suresh
Suresh does not own a car Uday does not own a bike Uday is a Lie-teller
I am not an Switcher I am not a Lie-teller Ramesh is a Truth-Speaker
Ramesh does not own a car Suresh does not own a cycle I own a cycle
SOLUTION: The most important information is there is only one Truth-Speaker:
Now we will proceed as follows:
  1. As Uday says” I am not a Switcher”. As discussed above he can be a truth speaker or a switcher.
  2. now we will proceed with self assumption method
(a)Let us first assume that he is a truth speaker
So,all his statements are true. So he will own a car as per his first and third statement neither of Ramesh or Suresh owns a car.
Now Ramesh’s last statement is true. So he can be a switcher or a truth speaker. Now since he cannot be a truth speaker (as only one truth speaker is there), he must be a switcher. So his second statement must be false. But it is true. So our assumption is wrong.
(b)Let us now take the second assumption that Uday is a Switcher.
So his second statement is false. So first and third are true. This proved that Uday owns a car.
Now see that last column of Suresh’s statements. His first statement is false. So he must be a lie teller or switcher.
Now it is given that there is exactly one truth speaker and now the only one person left is Ramesh. So he is a truth speaker. so we can conclude that his all three statements are true.
 As per his last statement “Suresh does not own a cycle”, we can conclude that Suresh owns a bike.
So we can now check that Suresh’s first and last statement is false and second statement is true .So he is a switcher. So we can conclude the following:
Uday Ramesh Suresh
Switcher Truth-Speaker Switcher
Car Cycle Bike
So, there are 2 Switchers and 1 Truth-Speaker.